Originally a twit was a person who annoys or "twits" others. Not unlike other tw words (twaddle, twat, twerp, etc.) and rhymes with nitwit

Now comes "twitter" and twit takes on a whole new definition. It is still someone who annoys others or "twits" them. But now it is someone so infatuated with twitter and their tweets that when not twittering they are talking about twitter and tweets. A twit is someone who has lost the ability to communicate face to face. Someone lacking interpersonal skills.